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Fifty fifth-grade students from each of four city schools were given a standardized fifth-grade reading test. After grading, each student was rated as satisfactory or not satisfactory in reading ability, with the following results:

1 2 3 4 School

7 10 13 6 Not satisfactory

Is there sufficient evidence to indicate that the percentage of fifth-grade students with an unsatisfactory reading ability varies from school to school?

Fifty fifth-grade students from each of four city schools were given a standardized fifth-grade reading test. After grading, each student was rated as satisfactory or not satisfactory in reading ability, with the following results:

1 2 3 4 School

7 10 13 6 Not satisfactory

Is there sufficient evidence to indicate that the percentage of fifth-grade students with an unsatisfactory reading ability varies from school to school?

Null hypothesis is that there is no variation between schools. Then the
expected number not-satisfactory in each school would be 9.

Then the statistic:

has a (approximatly) distribution with 3 degrees of freedom, where thes are the observed frequencies and are the expected frequencies.